Class 6 Maths Chapter 8: Playing with Constructions (Hinglish Notes)

Ye chapter kis baare mein hai?

Construction kuch instruments se bani ekdum sahi drawing hai: yahan ruler aur compass. Chapter circles aur curves se bane artwork se shuru hota hai, phir square aur rectangle pe aata hai: koi figure square ya rectangle kab hai, use kaise banayein, aur uske diagonals kya karte hain. Baar-baar ye kehta hai ki pehle rough diagram se plan karo, aur compass se points bina trial and error ke mark karo.

Circle aur compass

Ek point P mark karo, aur har disha mein bahut se points jo usse 4 cm door hon. Ye sab milkar circle banate hain. P uska centre hai, aur 4 cm, yaani centre se circle ke kisi bhi point tak ki doori, uska radius hai. Banane ke liye compass ko ruler ke saath 4 cm kholo, needle ko P pe tika ke rakho aur pencil ko poora ghumao. Circles aur half circles se Wavy Wave jaisa artwork banta hai: AB = 8 cm pe 2 cm radius ke do half circles AB ke dono aadhe hisson pe khade hote hain. Steps compass se circle kaise banayein mein dekho.

Square aur rectangle

Rectangle ABCD mein A, B, C aur D corners hain, AB, BC, CD aur DA sides hain, aur AB aur CD aamne-saamne ki sides hain. Rectangle ki do properties hain:

• R1: aamne-saamne ki sides barabar hoti hain, aur
• R2: saare angles 90° hote hain.

Square mein S1: saari sides barabar, aur S2: saare angles 90°. Naam mein corners figure ke chaaron taraf ghoomne ke kram mein likhe jaate hain, isliye ABCD, BCDA aur ADCB ek hi rectangle ke naam hain, par ABDC nahi. Ghumaya hua square ya rectangle bhi square ya rectangle hi rehta hai, kyunki ghumane se na lambai badalti hai na angles.

Square aur rectangle banana

6 cm side ka square PQRS banane ke liye PQ = 6 cm kheencho, P aur Q pe PQ ke perpendicular kheencho, compass se un par 6 cm pe S aur R mark karo, aur SR jodo. Rectangle bhi isi tarah do alag lambaiyon se banta hai. Aisi 4 sides wali figure nahi ban sakti jiske chaaron angles 90° hon par aamne-saamne ki sides barabar na hon: aamne-saamne ki sides hamesha barabar aati hain. Dekho rectangle aur square kaise banayein.

Rectangles mein ek exploration

Rectangle ABCD mein AB = 7 cm aur BC = 4 cm hai; X ko AD pe aur Y ko BC pe chalne do. XY sabse chhota, theek 7 cm, tab hota hai jab X aur Y, A aur B se barabar door hon; tab ABYX ek rectangle hai. XY sabse lamba tab hota hai jab wo aamne-saamne ke corners ko jode, yaani jab wo diagonal AC ya BD ho.

Rectangle ko 2 ek jaise squares mein tabhi toda ja sakta hai jab uski lambi side chhoti side ki 2 guna ho, aur 3 ek jaise squares mein tabhi jab 3 guna ho. Rough diagram dikhata hai ki kaun si sides barabar hain, aur compass ek lambai ko bina ruler ke doosri jagah copy kar deta hai.

Rectangle aur square ke diagonals

Rectangle PQRS ke aamne-saamne ke corners ko jodne wali lines PR aur QS uske diagonals hain, aur ye barabar hote hain. Diagonal jis corner se milta hai use do hisson mein baantta hai. Lambi sides ke paas ke chaaron hisse barabar hain, chhoti sides ke paas ke chaaron hisse barabar hain, aur har jodi milkar 90° banati hai. Sirf square mein dono hisse barabar hote hain: 45° aur 45°.

Iska istemaal do tarah ke constructions mein hota hai. Agar diagonal ko corners ko 60° aur 30° mein baantna hai, to AB, B pe perpendicular, aur A se AB ke saath 60° ki line kheencho; ye C pe milte hain. Agar ek side aur ek diagonal diye hon, to side kheencho, uske ek sire pe perpendicular, aur doosre sire se diagonal ki lambai ka arc, teesra corner dhoondhne ke liye.

Do points se barabar door points: House

House mein border ki har line 5 cm hai. Base ke baad aisa point A chahiye jo B aur C dono se 5 cm door ho. B se 5 cm door saare points B ke chaaron taraf ek circle pe hain, aur C se 5 cm door saare points C ke chaaron taraf ek circle pe, isliye A wahan hai jahan dono circles kaatte hain. Bas chhote arcs kaafi hain. Isi idea se aisi 4 sides wali figure banti hai jiski saari sides barabar hon par wo square na ho. Chapter ke har sawal ka jawab Chapter 8 ke NCERT solutions mein hai.